I hope this helps someone else who might come across this issue. I learned that if the table of contents has more than one layer with the same name, the Near Tool uses whichever is the top layer with that name. I often copy and paste layers to create different queries and different symbology so I usually have at least a couple layers with the same name. Once I placed the layer I wanted used for calculating proximity distances above its copy it gave the the results I needed. The tool must just do a layer name search and uses the first match it finds.
Again, if anyone else has similar issues and doesn't quite figure it out, I hope this helps.
Again, if anyone else has similar issues and doesn't quite figure it out, I hope this helps.